A chiral aperiodic monotile

作者：David John Smith, Joseph Samuel Myers, Craig S. Kaplan, Chaim Goodman-Strauss · 发表于：Combinatorial Theory · 年份：2024 · DOI：10.5070/c64264241 · 被引用次数：38 · 研究领域：Quasicrystal Structures and Properties、Matrix Theory and Algorithms、Advanced Materials and Mechanics

The recently discovered "hat" aperiodic monotile mixes unreflected and reflected tiles in every tiling it admits, leaving open the question of whether a single shape can tile aperiodically using translations and rotations alone. We show that a close relative of the hat--the equilateral member of the continuum to which it belongs--is a weakly chiral aperiodic monotile: it admits only non-periodic tilings if we forbid reflections by fiat. Furthermore, by modifying this polygon's edges we obtain a family of shapes called Spectres that are strictly chiral aperiodic monotiles: they admit only homochiral non-periodic tilings based on a hierarchical substitution system.Mathematics Subject Classifications: 05B45, 52C20, 05B50Keywords: Tilings, aperiodic order, polyforms